Since Hounsfield invented the first CT machine in 1972, CT technology has brought revolutionary influence to medical diagnosis and industrial non-destructive detecting. CT has become an important detecting means for industries of medical treatment, biology, aeronautics, astronautics, national defense, etc. With the improvement of the technology, CT scanning modes and imaging methodologies have been continually improved, and three-dimensional cone-beam CT has become the mainstream of research and application. X-ray cone-beam CT has been broadly applied in fields of clinical medicine, security inspection, non-destructive detecting, etc. In particular, because the cone-beam CT system based on circular orbit scanning is comparatively simple with respect to mechanics, electronic control, and so forth, and is easy for engineering realization, it is very broadly applied in clinical medicine, security inspection, and industrial non-destructive detecting. In circular-orbit cone-beam reconstruction methods, the most broadly applied method is FDK method proposed by Feldkamp et al. (Feldkamp L. A., L. C. Davis, and J. W. Kress, Practical cone-beam algorithm, Journal of the Optical Society of America, 1984, (1): 612-619).
The FDK method can be deemed as an approximate expansion to the fan-beam FBP (Filtered Backprojection) method under three-dimensional condition. The FDK method includes the following steps: initially implementing weighting processing on projection data; then implementing one-dimensional filtering on the projection data of different projection angles in the horizontal direction; and finally implementing three-dimensional back projection along the direction reverse to the X-ray to obtain a last three-dimensional reconstructed image of the object.
Thus, it can be seen that the reconstructed voxel values of the FDK method are based on the sum of the contribution of radiation passing through the voxel in the projection angle range of 360 degrees. Accordingly, the circular-orbit cone-beam FDK method, as an approximate method, has the characteristics where the mathematical formula is simple and the method computation is fast, and it is easy for engineering realization. Moreover, when the cone angle is comparatively small (generally within ±5°), it can achieve a very good reconstruction effect, and it is therefore broadly appreciated in practical engineering application.
However, the FDK method also has certain problems. Because the circular orbit scanning per se does not satisfy the condition of data completeness for cone-beam precise reconstruction, there exists the problem of Radon data loss. Thus, when the cone angle of the cone beam increases, the resulting image reconstructed by the FDK method will include serious cone beam artifact, and the FDK reconstruction value will decrease fast in a plane far away from the scanning orbit, such that the method is greatly limited in application in a CT imaging system having a flat panel detector.
In order to improve the quality of image reconstruction of a circular-orbit FDK method under a large cone angle, based on the FDK method, a plurality of improved FDK methods are proposed, including, for example, P-FDK (parallel FDK), T-FDK (tent-FDK), HT-FDK (hybrid tent-FDK), EFDK (extended FDK), etc. In these improved FDK methods, because P-FDK and T-FDK are simple and can be easily implemented in engineering, they are comparatively broadly applied, and are therefore described briefly below in greater detail.
The P-FDK method is to obtain parallel fan-beam projection data by rebinning cone-beam projection data, and then reconstructing a three-dimensional image of an object through a Filtered Backprojection Method. As shown in FIG. 1(a), which is a schematic diagram of a scan by a circular-orbit cone-beam CT system using a flat panel detector, S(β) indicates the location of the X-ray source on the circular orbit, β indicates the angular sampling location of projection on the circular orbit, P(β,a,b) indicates the projection data on the flat panel detector, (a,b) is a rectangular coordinate system defined on the flat panel detector for indicating the location coordinates of each X-ray projected on the detector, R is the radius of the circular orbit. FIG. 1(b) shows a rebinning of cone-beam projection into fan-beam projection of parallel beams using the P-FDK method. The black solid dots represent the X-ray source, on a central virtual detector, in regard of the rebinned projection data. Because the distances from the parallel fan beams to the virtual detector under the same angle are different, a row of projection on the original flat panel detector are not horizontal on the corresponding virtual detector anymore. Instead, they are on a curve convex along the central row of the virtual detector. Taking the flat panel detector as an example, the data rebinning formula of P-FDK is as follows:
                                                        P                              P                ⁢                                  -                                ⁢                FDK                                      ⁡                          (                              θ                ,                t                ,                b                            )                                =                      P            ⁡                          (                                                θ                  -                                      arcsin                    ⁢                                                                                  ⁢                                          t                      R                                                                      ,                                  tR                                                                                    R                        2                                            -                                              t                        2                                                                                            ,                b                            )                                      ,                            (        1        )            wherein θ indicates the sampling location of the rebinned projection data in angular direction after rebinning by P-FDK, (t,b) is the rectangular coordinate system on the central virtual detector after the rebinning, indicating the location coordinates of each X-ray on the virtual detector after the rebinning. The subsequent derivation processes of the present invention also takes the flat panel detector as an example, other types of detectors, such as, for example, a cylindrical surface detector, can be obtained by making corresponding changes based on the flat panel detector, details of the changes not being further described herein.
The P-FDK method differs from the FDK method only in that the P-FDK method includes rebinning into parallel fan-beams such that the process of calculating weighting coefficients is omitted during back projection, while the method is not different from the FDK method in image quality.
The T-FDK method proposed by Grass et al. in 2000 provides an improvement. T-FDK provides for rebinning for a second time in a vertical fan-beam plane, in addition to rebinning the cone-beam projection into parallel fan beams. That is, T-FDK provides for rebinning projection data in both the horizontal and vertical directions, ultimately causing the difference of T-FDK from P-FDK to be in that the direction of filtering the projection data according to T-FDK is along the horizontal direction of the central virtual detector, which is as shown in FIG. 1(c), rather than along the convex curve direction. The data rebinning formula of T-FDK method is as follows:
                                                        P                              T                ⁢                                  -                                ⁢                FDK                                      ⁡                          (                              θ                ,                t                ,                s                            )                                =                      P            ⁡                          (                                                θ                  -                                      arcsin                    ⁢                                                                                  ⁢                                          t                      R                                                                      ,                                  tR                                                                                    R                        2                                            -                                              t                        2                                                                                            ,                                                      sR                    2                                                                              R                      2                                        -                                          t                      2                                                                                  )                                      ,                            (        2        )            where θ indicates the sampling location of the rebinned projection data in angular direction after rebinning according to T-FDK, and (t,s) is the rectangular coordinate system on the central virtual detector after the rebinning according to T-FDK, indicating the location coordinates of each X-ray on the virtual detector after the rebinning.
T-FDK, compared to FDK, in one respect, is similar to P-FDK in that it provides for rebinning into parallel fan beams such that the weighting coefficient during back projection is omitted, and thus is more efficient with respect to calculation. Meanwhile, because the filtering of projection data according to the T-FDK method is implemented along the horizontal direction of the central virtual detector, it reduces cone beam artifact induced by increase of cone angle and improves image reconstruction quality, such that it is possible to realize accurate three-dimensional imaging of a large object using a large-area flat panel detector through circular-orbit scanning. Besides, there is another thought of improving the FDK method which uses conjugate rays in a circular-orbit scanning projection, different back projection weighting coefficients being selected for conjugate projection so as to improve the quality of the reconstructed image, and a comparatively good effect being also achieved.
With the gradual popularization of the flat panel detector, there are more and more new types of cone-beam CT systems that use a large-area flat panel detector, and the requirement for a large-cone-angle circular-orbit cone-beam CT image reconstruction method is even greater. Taking the dental cone-beam CT apparatus which is comparatively broadly applied in dental disease diagnosis at present as an example, three-dimensional dental CT imaging of a plurality of manufacturers at present use a flat panel detector of 20 cm×25 cm, the distance from the X-ray source to the detector is 70 cm, and the size of the cone angle corresponding to the circular orbit scanning is ±8.13°. Because doctors make disease diagnosis mainly dependent on CT value of image, i.e., pixel value of the reconstructed image, the requirement for reconstruction value of image from the medical-use CT is very high. Such large-cone-angle circular-orbit scanning goes far beyond the scope in which reconstruction can be done according to the FDK method, and the reconstruction result according to the T-FDK method is also unsatisfactory. Moreover, with the rapid development of the detector technology, detectors having an even larger-area flat panel have been applied in clinical use. For example, flat panel detectors of different sizes of 30 cm×40 cm, 43 cm×43 cm, etc. have been applied in clinical DR (Digital Radiography System). These detectors of even larger area can greatly improve the effective detection area of cone-beam X-ray, enlarge field of view of imaging, and most importantly, can reduce or even eliminate the problem where the CT value is unable to provide an accurate reconstruction due to truncation of cone-beam projection data. Therefore, a large-area flat-panel detector can be very broadly applied in current and future three-dimensional CT image apparatuses. However, with increase of the area of the flat panel detector, the cone angle of the three-dimensional CT system correspondingly increases, resulting in the difficult problem of how to eliminate serious cone beam artifact under a large cone angle.